CN114859732A - A Feedforward Compensation Active Disturbance Rejection Controller Based on Scheduling Signal and Its Design Method - Google Patents

Abstract

The invention discloses a feedforward compensation active disturbance rejection controller based on a dispatch signal and a design method thereof, aiming at solving the problem of poor control quality when a large inertia process is operated in a wide range and frequently changing working conditions. Active disturbance rejection controllers, including feedforward controllers, feedback controllers, compensation modules, and extended state observers. By introducing scheduling signals, variable parameter design and real-time adjustment of feedforward controller, feedback controller, compensation module and extended state observer are carried out respectively, and the dynamic model information of the controlled process under variable working conditions is used in this process. It can improve the adaptability of the ADRC to large inertia and variable working conditions. The structure of the control system is simple, the setting method is concise, and it has a good prospect of engineering application.

Description

A Feedforward Compensation Active Disturbance Rejection Controller Based on Scheduling Signal and Its Design Method

technical field

The invention relates to the technical field of industrial automation, in particular to a feedforward compensation active disturbance rejection controller based on a scheduling signal and a design method thereof.

Background technique

Active Disturbance Rejection Control (ADRC) is an advanced control method that combines classical PID control with modern control theory. The earliest ADRC is a nonlinear controller, which consists of three parts: tracking differentiator, nonlinear combination and extended state observer. However, the nonlinear ADRC is complex in structure and difficult to set the controller parameters, so the linear ADRC is widely used. The basic structure of linear ADRC includes two parts: Error-based Linear Function (ELF) and Extended State Observer (ESO). Compared with other advanced control algorithms, linear ADRC does not depend on the precise model of the controlled object, and has the advantages of simple structure, convenient tuning, good anti-disturbance performance and strong robustness, and has been applied and developed in the field of industrial process control in recent years.

However, when linear ADRC is applied to the automatic control of large-scale thermal processes, it mainly faces two problems. First, when the inertia and lag of the controlled process are large, the observation effect of ESO becomes poor, resulting in the unsatisfactory control effect of ADRC. ; Second, when the operating conditions of the controlled process change frequently in a large range, the ADRC control performance designed according to the rated operating conditions will deteriorate. The patent document CN107703746A proposes to use the linear combination of the derivative of each order of the set value as the feedforward control variable of ADRC, which can improve the tracking ability when the set value changes rapidly. Wang You et al. "Design of Linear Active Disturbance Rejection Controllers for High-Order Large Inertial Systems" (Control and Decision, March 2022) propose an ADRC control structure and parameter tuning method that uses model information for compensation, which improves ADRC's response to large Control effects of inertial processes. However, for solving the problems existing in the above thermodynamic process control, that is, when the inertia of the controlled process is large and the dynamic characteristics change significantly with the working conditions, the improvement of the control effect of the above method is limited.

SUMMARY OF THE INVENTION

The present invention provides a feedforward compensation active disturbance rejection controller based on a dispatch signal and a design method thereof, aiming at solving the problem of poor control quality when a large inertia process is operated in a wide range and frequently changing working conditions. Using the dynamic model information of the controlled process under variable working conditions, the variable parameter design and real-time adjustment of the feedforward controller, the feedback controller, the compensation module and the extended state observer can be carried out, which can improve the ADRC's ability to cope with large inertia and adaptability to changing conditions.

The present invention is realized through the following technical solutions.

One aspect of the present invention provides a feedforward compensation active disturbance rejection controller based on a scheduling signal, including a feedforward controller, a feedback controller, a compensation module and an extended state observer.

The feedforward controller is: u _Q (t)=F1(Q(t)), where u _Q (t) is the feedforward control quantity, Q(t) is the scheduling signal, and F1( ) is the feedforward function.

其中，u_C(t)为反馈控制器的输出，r(t)为设定值，z_i(t)(i＝1,2,…,m+1)为所述扩张状态观测器的输出，

和b₀(t)为可调参数，且随调度信号Q(t)变化而变化。The feedback controller is:

Among them, u _C (t) is the output of the feedback controller, r(t) is the set value, and z _i (t) (i=1, 2,...,m+1) is the output of the expanded state observer ,

and b ₀ (t) are adjustable parameters and vary with the scheduling signal Q(t).

The output u _C (t) of the feedback controller can be used as the input of the compensation module.

The compensation module is: u _TF (t)=F2 (u _C (t), T _F2 (t), p), wherein, u _TF (t) is the output of the compensation module, F2 ( ) is the compensation function, T _F2 (t) and p are adjustable parameters, and T _F2 (t) varies with the scheduling signal Q(t).

The output u _TF (t) of the compensation module can be used as the input of the expanded state observer.

The output of the feedback controller and the output of the feedforward controller constitute the control law of the active disturbance rejection controller, which is: u(t)= _uQ (t)+ _uC (t), where u(t ) is the control amount.

In the above technical solution, the expanded state observer is:

Among them, y(t) is the controlled variable, β _i (t) (i=1,2,...,m+1) is the adjustable parameter of the extended state observer, which changes with the change of the scheduling signal Q(t), b ₀ (t) is an adjustable parameter of the feedback controller.

In the above technical solution, the transfer function of the compensation function (that is, the frequency domain form of the compensation function) is:

Among them, F2(s) is the transfer function of the compensation function, and U _TF (s) and U _C (s) are the pull-types of the outputs u _TF (t) and u _C (t) of the compensation module and the feedback controller, respectively. Transformation, p is the transfer function order of the compensation function, T _F2 (t) and p are adjustable parameters, and the value of T _F2 (t) changes with the change of the scheduling signal Q(t).

Another aspect of the present invention provides a method for designing a feedforward compensation ADRC controller based on a scheduling signal, comprising the following steps:

S1, select the scheduling signal Q(t) according to the variable working condition characteristics of the controlled process, and obtain the functional relationship between the scheduling signal Q(t) and the feedforward control amount according to design calculations or field experiments;

S2, calculate the inverse function according to the functional relationship between the scheduling signal Q(t) and the feedforward control quantity, and obtain the feedforward function F1(·); calculate the feedforward control quantity u _Q (t)=F1 according to the feedforward function and the scheduling signal (Q(t));

S3, obtain dynamic information of variable working conditions of the controlled process;

S4, design the compensation module and its compensation function F2(·), and use the dynamic information of variable working conditions obtained in S3 to obtain the output of the compensation module u _TF (t)=F2(u _C (t), T _F2 (t) , p), where F2( ) is the compensation function, u _C (t) is the output of the feedback controller, and T _F2 (t) and p are adjustable parameters;

Designing an expanded state observer, the output of the compensation module can be used as the input of the expanded state observer, and the output _zi (t) (i=1, 2, . . . , m+1) of the expanded state observer is obtained;

S6, design a feedback controller, and calculate the feedback control variable u _C (t):

其中，r(t)为设定值，

和b₀(t)为可调参数；

Among them, r(t) is the set value,

and b ₀ (t) are adjustable parameters;

S7, form the control law of the active disturbance rejection controller, and obtain the control quantity of the active disturbance rejection controller through the feedforward control quantity and the feedback control quantity:

u(t)= _uQ (t)+ _uC (t).

In the above technical solution, the selection of the scheduling signal Q(t) simultaneously satisfies the following two conditions:

(1) It can characterize the variable working condition characteristics of the controlled process;

(2) It has a designable functional relationship with the feedforward control variable.

According to one of the embodiments, the method for obtaining dynamic information under variable operating conditions of the controlled process in step S3 includes:

According to the nonlinearity of the controlled process, the variable working condition range of the controlled process is divided into q segments, and the dynamic information of each segment is obtained and expressed by the controlled process transfer function (higher-order linear function) as:

Among them, s is the Laplace operator, Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively, and the subscript γ2 (γ2=1,2,...,q) is the number of the working condition, G _{p, γ2} (s) is the transfer function of the controlled process under the working condition γ2, K _γ2 is the system gain of the working condition γ2, T _γ2 is the time constant under the working condition γ2, n is the controlled process The order of the transfer function.

In the above technical solution, the transfer function of the compensation function is designed as:

Among them, F2(s) is the transfer function of the compensation function F2( ), U _TF (s) and U _C (s) are the pull transforms of u _TF (t) and u _C (t), respectively, and T _F2 (t ) and p are adjustable parameters.

In the above technical solution, the adjustable parameter T _F2 (t) is designed as:

T _F2 (t) = _γ (t) = F _Tγ (Q(t), {Q _r2 }, {T _γ2 }), (γ2=1,2,...,q),

Among them, {T _γ2 } is the time constant under each working condition in the dynamic information of variable working conditions, {Q _r2 } is the dispatching signal value under each working condition, Q(t) is the dispatching signal, and F _Tγ (·) is linear or a nonlinear function; T _γ (t) is the output of the function, representing the time constant corresponding to the scheduling signal Q(t).

In the above technical solution, the adjustable parameter p of the compensation function is designed as: p=n-m. where n is the order of the transfer function of the controlled process, and m is the order of the feedback controller.

In the above technical solution, the time domain form of the output u _TF (t) of the compensation module is:

Among them, ΔT is the calculation period, and k is the discrete time sequence.

In the above technical solution, the expanded state observer is designed as:

Among them, y(t) is the controlled variable, β _i (t) (i=1,2,...,m+1) is the adjustable parameter of the extended state observer, which changes with the change of the scheduling signal Q(t), b ₀ (t) is an adjustable parameter of the feedback controller.

In the above technical solution, the adjustable parameter β _i (t) (i=1, 2, . . . , m+1) of the expanded state observer can be selected as follows:

其中，T_γ(t)为调度信号Q(t)对应的时间常数。where ω _o (t) is the state observer bandwidth,

Among them, T _γ (t) is the time constant corresponding to the scheduling signal Q(t).

设计为：In the above technical solution, the adjustable parameters of the feedback controller

Designed to:

Wherein, m is the order of the feedback controller, ω _c (t) is the bandwidth of the feedback controller, and T _γ (t) varies with the scheduling signal Q(t).

In the above technical solution, the adjustable parameter b ₀ (t) of the feedback controller is designed as:

Among them, both T _γ (t) and K _γ (t) vary with the scheduling signal Q(t).

Among them, K _γ (t) is calculated as follows:

K _γ (t)=F _Kγ (Q(t),{Q _r2 },{K _γ2 },

where {K _γ2 } is the time constant under each working condition in the dynamic information of the controlled process variable working condition, {Q _r2 } is the dispatching signal value under each working condition, Q(t) is the dispatching signal, F _Kγ (·) is a linear or nonlinear function; K _γ (t) is the output of the function, which represents the system gain corresponding to the scheduling signal Q(t).

Compared with the prior art, the present invention includes the following advantages and beneficial effects:

Aiming at the large inertia controlled process with frequently changing working conditions, the present invention proposes a feedforward compensation active disturbance rejection controller and its design method based on dispatching signals. Real-time adjustment is made with the adjustable parameters of the extended state observer, and the dynamic model information of the controlled process under variable operating conditions is used to improve the adaptive capability of ADRC to large inertia and variable operating conditions. The structure of the control system is simple, the setting method is concise, and it has a good prospect of engineering application.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are For some embodiments of the present invention, those of ordinary skill in the art can also obtain other drawings according to these drawings.

FIG. 1 is a schematic structural diagram of a feedforward compensation ADRC controller based on a scheduling signal according to an embodiment of the present invention.

FIG. 2 is a schematic diagram showing the comparison of the controlled variable curves under rated operating conditions provided in Embodiment 1 of the present invention.

FIG. 3 is a schematic diagram showing the comparison of the rated operating condition control quantity curves provided in Embodiment 1 of the present invention.

FIG. 4 is a schematic diagram showing the comparison of controlled variable curves under variable working conditions provided in Embodiment 1 of the present invention.

FIG. 5 is a schematic diagram showing the comparison of the variable operating condition control variable curves provided in Embodiment 1 of the present invention.

FIG. 6 is a schematic diagram showing the comparison of the controlled variable curves under the lifting load provided in the second embodiment of the present invention.

FIG. 7 is a schematic diagram showing the comparison of the control amount curves under the lifting load provided in the second embodiment of the present invention.

In the picture:

r(t) is the set value, y(t) is the controlled variable, u _c (t) is the feedback control variable, u _Q (t) is the feedforward control variable, u(t) is the control variable, u _TF ( t) is the output of the compensation module, z ₁ (t)～z _m+1 (t) is the output of the extended state observer, and Q(t) is the scheduling signal.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

In addition, the terms "first", "second", etc. are used for descriptive purposes only, and should not be construed as indicating or implying relative importance or implying the number of indicated technical features. In the description of the following embodiments, the meaning of "plurality" is two or more, unless otherwise expressly and specifically defined.

A feedforward compensation ADRC controller based on scheduling signals provided by the present invention is suitable for ADRC control of a controlled process (or called a controlled object), including a feedforward controller, a feedback controller, a compensation Modules and extended state observers. The control system (system for short) of the present invention includes the ADRC and the controlled process of its application. As shown in Figure 1, in order to solve the problem of poor control quality when the large inertia process runs in a wide range of frequently changing working conditions, the present invention introduces scheduling signals in the design of the active disturbance rejection controller and uses the controlled process to change the working conditions. Based on the dynamic model information under different conditions, the variable parameter design and real-time adjustment of the feedforward controller, feedback controller, compensation module and extended state observer are carried out respectively, which improves the adaptability of the active disturbance rejection controller to large inertia and variable working conditions. .

The control law of the active disturbance rejection controller constructed by the present invention, that is, the control quantity of the active disturbance rejection controller is obtained through the feedforward control quantity and the feedback control quantity: u(t)=u _Q (t)+u _C (t ).

S1, select the scheduling signal

The scheduling signal Q(t) is selected according to the variable working condition characteristics of the controlled process, and the functional relationship between the scheduling signal Q(t) and the feedforward control quantity is obtained according to design calculations or field experiments.

The scheduling signal Q(t) can be selected according to the physical working mechanism of the controlled process, and the following two conditions must be satisfied at the same time:

(1) It can characterize the variable working condition characteristics of the controlled process, that is, it can characterize the expected working conditions in the variable load process of the controlled process. For example, the power generation load command of thermal power units.

(2) It has a designable functional relationship with the feedforward control quantity. For example, when the power generation load command of the thermal power unit is used as the dispatch signal, and the basic coal feeding quantity is used as the preset feedforward control quantity, it can be calculated in advance through design or on-site. The functional relationship between the power generation load command and the basic coal supply amount was obtained experimentally.

S2, design feedforward function and feedforward controller

The feedforward function F1(·) can be a linear function or a nonlinear function, and is designed according to the physical relationship between the feedforward control quantity and the scheduling signal. The function of the feedforward controller is that when the scheduling signal changes and the expected operating conditions of the controlled process change, the control quantity can change rapidly according to the change of the scheduling signal Q(t), which speeds up the response process of the control system.

The feedforward control quantity of the feedforward controller is: u _Q (t)=F1(Q(t)).

The feedforward function F1(·) can be obtained by calculating the inverse function according to the functional relationship between the scheduling signal Q(t) and the feedforward control amount.

得到前馈控制量(前馈控制器的输出)，其中，Q(t)为调度信号,k_f为代表前馈作用强弱的可调参数。According to the above step S1, the functional relationship between the feedforward control variable and the dispatch signal in the variable operating condition range can be obtained by design calculation or field experiment, that is, the feedforward function F1(·) can be determined by the inverse function. For example, if Q(t)=F1 _f (u(t)) is obtained from the steady state experiment, the feedforward function F1(·) can be designed and obtained by

The feedforward control quantity (the output of the feedforward controller) is obtained, where Q(t) is the scheduling signal, and k _f is an adjustable parameter representing the strength of the feedforward effect.

S3, obtain dynamic information of variable working conditions of the controlled process

According to the non-linearity of the controlled process, its variable working condition range is divided into q segments, and the dynamic information of each segment is represented by a linear high-order transfer function, that is, the controlled process transfer function, which is:

Among them, s is the Laplace operator, Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively, and the subscript γ2 (γ2=1,2,...,q) is the number of the working condition, F _{p, γ2} (s) is the transfer function of the controlled process in the working condition γ2, K _γ2 is the system gain of the working condition γ2, T _γ2 is the time constant under the working condition γ2, n is The order of the transfer function of the controlled process.

S4, design compensation module and compensation function

The function of the compensation module and the compensation function is to generate a dynamic compensation effect that matches the dynamic characteristics of the controlled process when the system operating conditions change and the scheduling signal changes, and send it to the expanded state observer to reduce the state observation error and improve the controller. Control effects on large inertial processes.

The design of the compensation function F2(·) is based on the dynamic information of the controlled process obtained above, and can be expressed in the form of frequency domain or time domain.

The frequency domain form of the compensation function, that is, the transfer function is:

where F2(s) is the transfer function of the compensation function, U _TF (s) and U _C (s) are the pull transforms of u _TF (t) and u _C (t), respectively, and T _F2 (t) and p are Tunable parameter.

The time domain form of the output u _TF (t) of the compensation module is:

Among them, ΔT is the calculation period, and k is the discrete time sequence.

The adjustable parameters in the compensation function are T _F2 (t) and p. In the present invention, the selection method is as follows:

The value of T _F2 (t) changes with the scheduling signal Q(t), the purpose is to match the variation law of the dynamic characteristics of the controlled process with the working conditions, thereby reducing the equivalent observed object order of the extended state observer and improving the state observation Therefore, the real-time value of T _F2 (t) is determined according to the dynamic information of the controlled process and the scheduling signal, namely:

T _F2 (t)=T _γ (t)=F _Tγ (Q(t),{Q _r2 },{T _γ2 }),(γ2=1,2,...,q)

Among them, {T _γ2 } is the time constant under each working condition in the dynamic information of variable working conditions, {Q _r2 } is the dispatching signal value under each working condition, Q(t) is the dispatching signal, and F _Tγ (·) is linear or a nonlinear function, T _γ (t) is the output of the function, which represents the time constant corresponding to the scheduling signal Q(t).

The choice of the adjustable parameter p depends on the order of the ADRC adopted. If the order of the controlled process is n, the order of the ADRC is m, then the order of the extended state observer is m+1, and the order p of the compensation module should be taken as: p=n-m. This selection method enables all states not included in the compensation module to be observed by the extended state observer.

S5, Design an Extended State Observer

The time domain form of the extended state observer is as follows:

β _i (t) (i=1,2,...m+1) is the adjustable parameter of the extended state observer, and b0(t) is the adjustable parameter of the feedback controller, both of which change with the scheduling signal Q(t).

In the programmable control system, the Euler method is used to discretize the extended state observer, and its expression is as follows:

Among them, ΔT represents the calculation period, and k represents the discrete time sequence.

The adjustable parameter β _i (t) (i=1,2,...,m+1) of the extended state observer is selected as follows:

其中，T_γ(t)为调度信号Q(t)对应的时间常数。where ω _o (t) is the bandwidth of the extended state observer,

Among them, T _γ (t) is the time constant corresponding to the scheduling signal Q(t).

S6, Design the Feedback Controller

The feedback control variable is calculated by the feedback controller based on the set value and the output of the expanded state observer:

和b₀(t)为反馈控制器的可调参数，均随调度信号Q(t)变化。其中

可以按照带宽参数化方法，根据控制器带宽ω_c(t)计算得出，也可以通过优化算法或现场试验确定。b₀(t)是对被控过程高阶增益的估计值，随调度信号Q(t)变化。反馈控制器的作用是在工况变化或扰动发生时，反馈控制器能够根据设定值和扩张状态观测器的输出，对控制量进行调整，抵消观测到的总扰动并最终消除控制偏差。Among them, u _C (t) is the feedback control amount, r(t) is the set value of the control system, z _i (t) (i=1, 2,...,m+1) is the expansion state observer output,

and b ₀ (t) are adjustable parameters of the feedback controller, and both vary with the scheduling signal Q(t). in

It can be calculated from the bandwidth ω _c (t) of the controller according to the bandwidth parameterization method, or can be determined through optimization algorithms or field experiments. b ₀ (t) is an estimate of the higher-order gain of the controlled process, which varies with the scheduling signal Q(t). The function of the feedback controller is that when the working conditions change or disturbance occurs, the feedback controller can adjust the control quantity according to the set value and the output of the expanded state observer, offset the observed total disturbance and finally eliminate the control deviation.

设计为：Adjustable parameters of the feedback controller

Designed to:

where m is the order of the feedback controller, ω _c (t) is the bandwidth of the feedback controller, and T _γ (t) varies with the scheduling signal Q(t).

The adjustable parameter b ₀ (t) of the feedback controller is designed as:

Among them, both T _γ (t) and K _γ (t) vary with the scheduling signal Q(t).

K _γ (t) is calculated as follows:

K _γ (t)=K _Kγ (Q(t),{Q _r2 },{K _γ2 }

where {K _γ2 } is the time constant under each working condition in the dynamic information of the controlled process variable working condition, {Q _r2 } is the dispatching signal value under each working condition, Q(t) is the dispatching signal, F _Kγ (·) is a linear or nonlinear function, and K _γ (t) is the output of the function, which represents the system gain corresponding to the scheduling signal Q(t).

For convenience, the functions F _Kγ (·) and F _Tγ (·) can be taken as linear interpolation functions.

Then the control quantity of the feedforward compensation ADR controller based on the scheduling signal is the sum of the feedforward control quantity and the feedback control quantity, namely:

u(t)= _uQ (t)+ _uC (t).

The following two simulation examples are used as examples to illustrate the control effect of the present invention.

Example 1: Under rated operating conditions, the transfer function of the controlled object of the main steam pressure of a coal-fired unit is:

When the working conditions change, the time constant T varies between 30-50.

In order to illustrate the control effect of the present invention, firstly adopt the method of the present invention and take k _f =0 for design, and compare with conventional ADRC and comparative example 1 (patent document CN107703746A) ADRC with set value feedforward and comparative example 2 (Wang You et al., Design of Linear Active Disturbance Rejection Controller for Higher-Order Large Inertia Systems, Control and Decision Making, March 3, 2022, https://doi.org/10.13195/j.kzyjc.2021.1576) Compensation ADRC Compared.

Taking the order of the feedback controller as m=2, according to the design method of the present invention, the order of the extended state observer is m+1=3, and the order of the compensation function is nm=3. Under rated operating conditions, take the compensation function time constant T _F2 as 50, the controller bandwidth as 0.02, the expansion state observer bandwidth as 1, the control parameters as b ₀ =1.12×10 ^-5 , β ₁ =3, β ₂ = 3, β ₃ =1, k ₁ =4×10 ⁻⁴ , k ₂ =0.04. Under rated operating conditions, the traditional ADRC and the ADRC of Comparative Example 1 are designed, the controller bandwidth is 0.02, the expansion state observer bandwidth is 0.2, the control parameters are b ₀ =2.0158×10 ^-4 , β ₁ =0.6, β ₂ = 0.12, β ₃ =0.008, k ₁ =4×10 ⁻⁴ , k ₂ =0.04. The control effects of the above three methods are simulated.

Figure 2 shows the setpoint step response and disturbance response curves under rated operating conditions. At 1000 seconds, the set value has a unit step change, and at 5000 seconds, the input quantity of the controlled process has a step disturbance with an amplitude of 0.5. It can be seen from the curve that the ADRC with compensation designed by the present invention can reach the set value faster than the conventional ADRC and the ADRC with set value feedforward in Comparative Example 1 when the set value is changed stepwise. and no overshoot. When the input of the controlled process is disturbed, the ADRC designed by the present invention can eliminate the influence of the disturbance faster, and meanwhile the dynamic deviation is also minimized.

Figure 3 is the change curve of the control quantity under the rated working condition. It can be seen that the ADRC control quantity with compensation designed by the present invention changes more rapidly and steadily. The ADRC control quantity of Comparative Example 1 fluctuates too much instantaneously during the set value step response, while the conventional ADRC control quantity is obviously slow.

Figure 4 is the comparison curve of the set value step response and the disturbance response when the working condition changes to T=30. The second-order compensation ADRC of Comparative Example 2 is added here, and its parameters are consistent with the parameters of the ADRC of the present invention under rated operating conditions, but do not change with the operating conditions. It can be seen that the variable-parameter ADRC with compensation designed by the present invention can make the controlled variable reach the new set value more quickly and smoothly without overshoot because the control parameters change with the working conditions; the ADRC with compensation in Comparative Example 2 The setpoint tracking is slightly slower, and the ADRC with setpoint feedforward and conventional ADRC of Comparative Example 1 have the slowest response. At the same time, when the disturbance occurs, the ADRC of the present invention and the ADRC of the comparative example 2 have the same anti-disturbance capability, and both can eliminate the influence of the disturbance faster, and the dynamic deviation is also smaller.

Fig. 5 is the comparison curve of the control amount when the working condition changes to T=30. It can be seen that, compared with the other three methods, the change of the control amount of the ADRC of the present invention is both rapid and stable, that is, it does not cause an impact on the actuator, and can act in time, showing good engineering applicability.

It should be noted that in the above simulation, the second-order compensation ADRC controller based on the scheduling signal designed by the present invention does not set the feedforward function, so the curve comparison reflects the compensation ADRC control effect based on the scheduling signal. It can be seen from the simulation comparison results that the ADRC designed by the present invention is faster and more stable in setting value tracking than the compensation ADRC in Comparative Example 2, the conventional ADRC and the ADRC with set value feedforward in Comparative Example 1. In addition, there is no overshoot, the influence of disturbance can be eliminated more quickly, and the dynamic deviation is also small, which shows the excellent performance of the method of the present invention.

Embodiment 2: The controlled quantity of the main steam pressure circuit of a coal-fired unit is the main steam pressure, the control quantity is the coal feeding quantity, and the transfer function is a high-order inertial form:

where n=5. The load, coal feed, main steam pressure under each steady state condition, and model parameters K _γ2 and T _γ2 of the controlled process under this condition are shown in the table below.

load 0 99 165 250 330 coal supply 70 70 115 168 220 main steam pressure 0 9.5 13 16.5 19 K_γ2 0.1357 0.1357 0.1130 0.0982 0.0864 T_γ2 400 300 250 220 200

In order to illustrate the control effect of the present invention, a feedforward compensation ADRC controller based on the scheduling signal is designed according to the method of the present invention, and the controller order is taken as m=1. Taking the load command as the scheduling signal Q(t), referring to the model information and steady state under each working condition, and taking k _f =0.5, the feedforward controller is designed as follows:

According to the dynamic information of variable working conditions of the controlled process, the compensation function is determined as p=4th-order inertial link, and its form is as follows:

Among them, the time constant of the compensation function changes with the scheduling signal as follows:

The extended state observer is designed to be second-order, and its observer bandwidth ω _o (t) varies with the scheduling signal:

The tunable parameters of the extended state observer vary with ω _o (t):

The bandwidth ω _c (t) and tunable parameters of the feedback controller vary with the scheduling signal as follows:

k _p (t) = ω _c (t)

The simulation calculation period is ΔT=0.2s, the working condition value first decreases in stages and then increases in stages, the change rate is 0.055/s, and the set value changes with the working conditions. At the same time, in order to compare and illustrate the beneficial effects of the present invention, the compensation ADRC based on the scheduling signal with k _f =0, that is, without feedforward, and the compensation ADRC without the scheduling signal of Comparative Example 2 are also designed respectively, and the controller order is both taken as 1 . When the load changes, the variation curves of the controlled variable and the controlled variable obtained by the simulation are shown in Figure 6 and Figure 7, respectively.

It can be seen from FIG. 6 that the feedforward compensation ADRC based on the scheduling signal of the present invention can quickly and smoothly track the change of the set value no matter in the high load section, the middle load section or the low load section, and the adjustment time is significantly faster than Two other control methods. When k _f = 0, the control parameters of the compensation ADRC based on the dispatch signal without feedforward can change with the load, so it shows a relatively consistent smooth control effect under different working conditions, but because there is no feedforward controller, it completely relies on The feedback effect is used to adjust, so the response speed is significantly slower than that of the feedforward compensation ADRC controller based on the scheduling signal. The controlled variable of the compensation ADRC without scheduling signal in Comparative Example 2 can track the change of the set value relatively smoothly in the high load section, but because there is no signal scheduling mechanism, the control parameters do not change with the working conditions, so it appears in the low load section. A significantly larger overshoot occurs. Based on the above comparison results, it can be seen that when the working conditions change in a large range, the feedforward compensation ADRC based on the dispatching signal designed by the present invention can show a relatively consistent and satisfactory control effect under each load, showing excellent working conditions. adaptability and excellent control effect.

It can be seen from the change curve of the control quantity in FIG. 7 that the control quantity of the ADRC of the present invention is also fast and stable under various working conditions, so it has a very good engineering application prospect.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features thereof can be equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the technical solutions of the embodiments of the present invention. scope.

Claims (10)

1. A feedforward compensation active disturbance rejection controller based on a dispatch signal, characterized in that, comprising a feedforward controller, a feedback controller, a compensation module, and an expanded state observer; The feedforward controller is: u _Q (t)=F1(Q(t)), where u _Q (t) is the feedforward control quantity, Q(t) is the scheduling signal, and F1( ) is the feedforward function; The feedback controller is:

Among them, u _C (t) is the output of the feedback controller, r(t) is the set value, and z _i (t) (i=1, 2, ..., m+1) is the output of the expanded state observer ,

and b ₀ (t) are adjustable parameters and vary with the scheduling signal Q(t); The compensation module is: u _TF (t)=F2(u _C (t), T _F2 (t), p), wherein u _TF (t) is the output of the compensation module, F2( ) is the compensation function, u _C (t) is the output of the feedback controller, T _F2 (t) and p are adjustable parameters, and T _F2 (t) changes with the change of the scheduling signal Q(t); the output of the compensation module u _TF (t) can be used as an input to the expanded state observer; The output of the feedback controller and the output of the feedforward controller constitute the control law of the active disturbance rejection controller, which is: u(t)= _uQ (t)+ _uC (t), where u(t ) is the control amount. 2. The active disturbance rejection controller according to claim 1, wherein the expanded state observer is:

Among them, y(t) is the controlled variable, β _i (t) (i=1, 2, ..., m+1) is the adjustable parameter of the extended state observer, which changes with the change of the scheduling signal Q(t), b ₀ (t) is an adjustable parameter of the feedback controller. 3. The active disturbance rejection controller according to claim 1, wherein the transfer function of the compensation function is:

Among them, F2(s) is the transfer function of the compensation function, and U _TF (s) and U _C (s) are the pull-types of the outputs u _TF (t) and u _C (t) of the compensation module and the feedback controller, respectively. Transformation, p is the transfer function order of the compensation function, T _F2 (t) and p are adjustable parameters, and the value of T _F2 (t) changes with the change of the scheduling signal Q(t). 4. A design method of a dispatch signal-based feedforward compensation ADRC controller according to any one of claims 1 to 3, characterized in that, comprising: S1, select the scheduling signal Q(t) according to the variable working condition characteristics of the controlled process, and obtain the functional relationship between the scheduling signal Q(t) and the feedforward control amount according to design calculations or field experiments; S2, calculate the inverse function according to the functional relationship between the scheduling signal Q(t) and the feedforward control quantity, and obtain the feedforward function F1(·); calculate the feedforward control quantity u _Q (t)=F1 according to the feedforward function and the scheduling signal (Q(t)); S3, obtain dynamic information of variable working conditions of the controlled process; S4, design the compensation module and the compensation function F2(·), and use the dynamic information of the variable working conditions obtained in S3 to obtain the output of the compensation module u _TF (t)=F2 (u _C (t), T _F2 (t), p), where F2( ) is a compensation function, u _C (t) is the output of the feedback controller, and T _F2 (t) and p are adjustable parameters; S5, design an expanded state observer, the output of the compensation module can be input as an expanded state observer, and obtain the output _zi (t) (i=1, 2, . . . , m+1) of the expanded state observer; S6, design a feedback controller, and calculate the feedback control variable u _C (t):

Among them, r(t) is the set value,

and b ₀ (t) are adjustable parameters; S7, construct the control law of the active disturbance rejection controller, and obtain the control quantity of the active disturbance rejection controller through the feedforward control quantity and the feedback control quantity: u(t)= _uQ (t)+ _uC (t). 5. The design method according to claim 4, wherein the selection of the scheduling signal Q(t) satisfies the following two conditions simultaneously: (1) It can characterize the variable working condition characteristics of the controlled process; (2) It has a designable functional relationship with the feedforward control variable. 6. The design method according to claim 4, characterized in that, the method for obtaining dynamic information of variable working conditions of the controlled process comprises: According to the nonlinearity of the controlled process, the variable operating condition range of the controlled process is divided into q segments, and the dynamic information of each segment is obtained and expressed by the controlled process transfer function as:

Among them, s is the Laplace operator, Y(s) and U(s) are the Laplace transforms of y(t) and u(t), respectively, and the subscript γ2 (γ2=1, 2, ..., q) is the working condition number, G _{p, γ2} (s) is the transfer function of the controlled process under working condition γ2, K _γ2 is the system gain of working condition γ2, T _γ2 is the time constant under working condition γ2, and n is the order. 7. The design method according to claim 4, wherein the transfer function of the compensation function is:

Among them, F2(s) is the transfer function of the compensation function F2( ), U _TF (s) and U _C (s) are the pull transforms of u _TF (t) and u _C (t), respectively, and T _F2 (t ) and p are adjustable parameters. 8. The design method according to claim 4, wherein the time domain form of the output u _TF (t) of the compensation module is:

Among them, ΔT is the calculation period, and k is the discrete time sequence. 9. The design method according to claim 4, wherein the expanded state observer is designed as:

Among them, y(t) is the controlled variable, β _i (t) (i=1, 2, ... m+1) is an adjustable parameter, which changes with the change of the scheduling signal Q(t), and b ₀ (t) is Adjustable parameters of the feedback controller. 10. The design method according to claim 4, wherein the adjustable parameters of the feedback controller

for:

Wherein, m is the order of the feedback controller, ω _c (t) is the bandwidth of the feedback controller, and T _γ (t) varies with the scheduling signal Q(t).

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